Service is regarded as the most crucial shot in tennis matches, and hence affects the outcome. This study aims to construct a mathematical model that expresses the scoring probability of service shots. Here, “scoring” means that the server wins points in subsequent rallies after a service. The explanatory variables are the service landing location and the ranking points of the players (logarithms of ranking points for the two players). The model construction method is a stepwise regression of the generalized linear model. The model is constructed using more than 110,000 service shots from Association of Tennis Professionals Tour tournaments of 2019. The model comprises four service situations: first/second and ad/deuce sides. The developed model reveals the following facts: in the first service, advantageous locations for the servers are not symmetric between the advantage and deuce sides. Higher-ranked players can win more points than lower-ranked players even if their shots land in easy locations, that is, in the middle of the service court.

中文翻译：

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男子职业网球比赛中基于发球位置和排名积分的得分概率模型

发球被认为是网球比赛中最关键的一击，影响着比赛的结果。本研究旨在构建一个表达发球得分概率的数学模型。这里的“得分”是指发球方在发球后的后续比赛中得分。解释变量为服务落地地点和玩家排名积分（两名玩家排名积分的对数）。模型构建方法是广义线性模型的逐步回归。该模型使用 2019 年职业网球协会巡回赛中超过 110,000 个发球镜头构建。该模型包括四种发球情况：第一/第二和正/平局。所开发的模型揭示了以下事实：在第一种服务中，服务器的有利位置在优势方和劣方之间不对称。排名较高的球员可以比排名较低的球员赢得更多的分数，即使他们的击球落在容易的位置，即发球区的中间。